Cut singularity of compressible Stokes flow. (English) Zbl 1519.35243
Summary: In this paper we study the cut singularity governed by a compressible Stokes system. The cut is a non-Lipshitz boundary. The divergence of the leading corner singularity vector, which has the singular exponent 1/2, has different trace values on either side of cut. In the consequence the pressure solution of the continuity equation must have a jump across the streamline emanating from the cut tip. We establish a piecewise regularity of the solution by the corner singularity and the contact singular function.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76F50 | Compressibility effects in turbulence |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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